Method and apparatus for codebook-based feedback in a closed loop wireless communication system

ABSTRACT

A method and apparatus are provided for feedback for closed-loop transmitting with multiple transmit antenna elements and multiple receive antenna elements. A base station includes a codebook containing sets of weightings for the multiple transmit antenna elements, with each set of weightings identified by an index and the codebook known to the base station and a served mobile station (MS). The base station pre-codes pilot signals using a precoding matrix, preferably a unitary matrix, to produce pre-coded pilot signals, which precoding matrix may or may not be known to the MS and which precoding matrix may or may not be included in the codebook. The base station then transmits the pre-coded pilot signals to the MS via the multiple transmit antenna elements and, in response, receives an index to a set of weightings in the codebook for use in a subsequent transmission of a data stream.

FIELD OF THE INVENTION

The present invention relates generally to wireless communicationsystems, and in particular, to a method and apparatus for providingcodebook-based feedback in a closed loop wireless communication system.

BACKGROUND OF THE INVENTION

Wireless communication system transmission methods have evolved toinclude multiple transmit antennas and multiple receive antennas inorder to greatly increase the link capacity of wireless communicationsystems and/or to better focus the transmitted energy at the receiverfor greater efficiency and less interference. An antenna array is agroup of spaced apart antenna elements that each transmits an antennasignal that has a specific gain and phase relationship with the otherantenna signals. When the antenna elements work together transmittingthe antenna signals, they produce an antenna pattern that is morefocused on the receiver than a pattern produced by a single antennaelement. The process of changing the gain and phase of a signal toproduce antenna signals may be referred to as “weighting” the signalusing a set of “antenna array weights.” Because antenna arrays maysimilarly be used at a receiver to improve signal quality, use ofantenna arrays at both the transmitter and receiver has been proposed.When multiple antenna elements are used at each of the transmitter andreceiver, the wireless channel between them may be referred to as amultiple-input, multiple-output (MIMO) channel. Determining how to feedsignals to the multiple transmit antenna elements and receive signalsfrom the multiple receive antenna elements becomes quite complicated.

Various transmission strategies require the transmit antenna array tohave some level of knowledge concerning the channel response betweeneach transmit antenna element and each receive antenna element and areoften referred to as “closed-loop” MIMO. Obtaining full broadbandchannel knowledge at the transmitter is possible using techniques suchas uplink sounding in Time Division Duplexing (TDD) systems and channelfeedback in either TDD or Frequency Division Duplexing (FDD) systems.Limited feedback methods, such as fixed beam selection or codebook-basedbeamforming weight selection, can reduce the amount of feedback asopposed to full channel feedback, which would require a significantamount channel resources thereby reducing the link capacity.

Codebook-based beamforming weight selection involves selection, by abase station based on feedback from a mobile station, of a set ofpre-coding matrices, that is, predetermined beamforming weights that areagreed upon between a transmitter and receiver. The weights are selectedfrom a set, or codebook, of predetermined and agreed upon matrices ofbeamforming weights. Each matrix in the codebook can be identified by anindex, and a mobile station identifies the weights to be applied byfeeding back an index to a matrix and rank of the matrix. In this way,only an index and a rank need be used in feedback to the transmitter inorder for the transmitter to know the proper weights to use.

In order to provide such feedback, a base station conveys a midamble,that is, a predetermined signal, to a mobile station (MS). The midambleis not weighted, that is, no beamforming weights are applied to themidamble prior to transmission to the MS. Based on the receivedmidamble, the MS computes a channel response for the air interfacebetween the mobile station and the base station and, based on thechannel response, determines a matrix and rank of weights forapplication to downlink transmissions. However, existing codebooks arequite complex, with weights for each index comprising a matrix of a rankof up to the number of antenna elements (the rank means the number ofdata streams that are to be transmitted). Selecting, by an MS, a matrixand rank for application to downlink transmissions requires a number ofinvolved calculations, which can include complex math including matrixmultiplications. For example, for codebook feedback by an MS,computations scale by at least a factor M_(t)N as the number of antennaelements increases, where M_(t) is the number of transmit antennaelements at a base station and N is a number of indices in the codebookfor each rank. For fixed beam selection, use of a precoded midamblereduces computational complexity but requires an increased midamblesize, and correspondingly reduced downlink throughput, as compared tocodebook techniques. That is, as a number of transmit antenna elementsincreases, midamble overhead scales as N for beam selection but as M_(t)for codebook feedback. For example, for four transmit antenna elementsM_(t)=4 and N=16, and for eight transmit antennas elements M_(t)=8 andN=64.

Therefore, there is a need for a method and apparatus of closed loopfeedback that reduces the computational complexity of the searchingrequired for determining a codebook index and rank to feedback to thebase station and that will not increase downlink overhead over thecurrent art.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a high-level schematic diagram of a wireless communicationschannel in accordance with an embodiment of the present invention.

FIG. 2 is a high-level block diagram of a two-input, two-output MIMOchannel in accordance with an embodiment of the present invention.

FIG. 3 is a block diagram of a wireless communication system thatemploys a multiple-stream, multiple-antenna (MIMO) wirelesscommunication scheme in accordance with an embodiment of the presentinvention.

FIG. 4 is a block diagram of a multiple-stream, multiple-antenna basestation of FIG. 3 in accordance with an embodiment of the presentinvention.

FIG. 5 is a block diagram of an antenna array signal processor of thebase station of FIG. 4 in accordance with an embodiment of the presentinvention.

FIG. 6 is a block diagram of a multiple-stream, multiple-antenna mobilestation of FIG. 3 in accordance with the method and system of thepresent invention.

FIG. 7 is a logic flow diagram of method performed by the communicationsystem of FIG. 3 for precoding of a pilot signal in accordance with anembodiment of the present invention.

FIG. 8 is a graphical representation of error rate results in accordancewith the present invention compared to the prior art.

FIG. 9 is a logic flow diagram that illustrates a method performed bythe mobile station of FIG. 3 in determining an effective channel for oneor more matrices of a codebook in accordance with an embodiment of thepresent invention.

One of ordinary skill in the art will appreciate that elements in thefigures are illustrated for simplicity and clarity and have notnecessarily been drawn to scale. For example, the dimensions of some ofthe elements in the figures may be exaggerated relative to otherelements to help improve understanding of various embodiments of thepresent invention. Also, common and well-understood elements that areuseful or necessary in a commercially feasible embodiment are often notdepicted in order to facilitate a less obstructed view of these variousembodiments of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

To address the need for a method and an apparatus that provides closedloop feedback that reduces the computational complexity of the searchingrequired for determining a codebook index and rank to feedback to a basestation and that will not increase downlink overhead over the currentart, a method and apparatus are provided for feedback for closed-looptransmitting with multiple transmit antenna elements and multiplereceive antenna elements. A base station includes a codebook containingsets of weightings for the multiple transmit antenna elements, with eachset of weightings identified by an index and the codebook known to thebase station and a served mobile station (MS). The base stationpre-codes pilot signals using a precoding matrix, preferably a unitarymatrix, to produce pre-coded pilot signals, which precoding matrix mayor may not be known to the MS and which precoding matrix may or may notbe included in the codebook. The base station then transmits thepre-coded pilot signals to the MS via the multiple transmit antennaelements and, in response, receives an index to a set of weightings inthe codebook for use in a subsequent transmission of a data stream.

Generally, an embodiment of the present invention encompasses a methodfor providing feedback for closed-loop transmitting with multipletransmit antenna elements and multiple receive antenna elements. Themethod includes providing a codebook containing sets of weightings forthe multiple transmit antenna elements with each set of weightingsidentified by an index and the codebook known to a transmitter and areceiver, pre-coding pilot signals using a precoding matrix to producepre-coded pilot signals, transmitting the pre-coded pilot signals to thereceiver via the multiple transmit antenna elements, and in response totransmitting the pre-coded pilot signals, receiving at the transmitteran index to a set of weightings in the codebook for use in a subsequenttransmission of a data stream.

Another embodiment of the present invention encompasses a method forproviding feedback for closed-loop transmitting with multiple transmitantenna elements and multiple receive antenna elements. The methodincludes receiving pre-coded pilot signal determining effective channelsfor a subset of rank-1 codebook weightings to produce ‘S’ effectivechannels, and determining an effective channel for each remainingcodebook weightings as a low complexity function of the ‘S’ effectivechannels.

Yet another embodiment of the present invention encompasses a basestation that is capable of operating in a multiple input, multipleoutput communication system. The base station includes an antenna arraycomprising multiple antenna elements, a codebook containing sets ofweightings for the multiple transmit antenna elements with each set ofweightings identified by an index known to the base station and a mobilestation serviced by the base station, an antenna array signal processorthat pre-codes pilot signals using a matrix to produce pre-coded pilotsignals that is transmitted via the plurality of transmit antennaelements, and a receiver that receives an index to a set of weightingsin the codebook for use in a subsequent transmission of a data stream.

Still another embodiment of the present invention encompasses a mobilestation that is capable of operating in a multiple input, multipleoutput communication system, the mobile station comprising multipleantenna elements and configured to receive a pre-coded pilot signal,based on the received pilot signal, determine an effective channel for asubset of rank-1 codebook weightings to produce ‘S’ effective channels,and determine an effective channel for each remaining codebookweightings as a function of the ‘S’ effective channels.

In the present invention, the communication system may utilize anOrthogonal Frequency Division Multiplexed (OFDM) or multicarrier basedarchitecture including Adaptive Modulation and Coding (AMC). Thearchitecture may also include the use of spreading techniques such asmulti-carrier CDMA (MC-CDMA), multi-carrier direct sequence CDMA(MC-DS-CDMA), Orthogonal Frequency and Code Division Multiplexing(OFCDM) with one or two dimensional spreading, or may be based onsimpler time and/or frequency division multiplexing/multiple accesstechniques, or a combination of these various techniques. However,alternate embodiments of the communication system may utilize othercellular communication system protocols such as, but not limited to,TDMA, direct sequence CDMA, cyclic prefix single carrier systems,interleaved frequency division multiple access systems.

The present invention may be more fully described with reference toFIGS. 1-9. FIG. 1 shows a high-level schematic diagram of a wirelesscommunications channel. As shown, x represents user data that will bewirelessly transmitted to the receiver. At the receiver, {circumflexover (x)} represents an estimate of the data transmitted, x. User data xmay be split in the transmitter to produce a vector that representsmultiple data streams, x₁, x₂, . . . x_(N).

User data x is processed by a matrix V to produce adaptive array antennasignals z. Each column of matrix V is a vector containing an antennaarray weight set used to transmit one of the data streams x_(i). Signalsz are wirelessly transmitted from antenna elements of a transmit antennaarray, and received at a receiver antenna array as received antennasignals r. The air interface or channel between antenna signals z andreceived antenna signals r includes matrix H, which describes theeffects of the air interface or channel on signals z. Received antennasignals r are processed in the receiver by matrix T′ to produce theestimate of the data, {circumflex over (x)}.

Referring now to FIG. 2, there is depicted a two-input, two-output MIMO(multiple input, multiple output) antenna array system, although itshould be recognized that the present invention is not limited to a twoantenna system and can be applied equally well to any number of transmitand receive antennas. This MIMO system in this example is used tosimultaneously transmit two different data streams, z₁ and z₂, to asingle mobile station through a “composite channel” H, defined by thematrix

$H = \begin{bmatrix}h_{11} & h_{12} \\h_{21} & h_{22}\end{bmatrix}$where h_(mn), m=1, 2, and n=1, 2, are complex channel values. Note thatthe term “composite channel” as used herein refers to a completemeasurement or description of a channel, wherein the effects of allcombinations of transmit antennas and receive antennas are considered.The composite channel may be thought of as the aggregation of allchannels and precoding weights between arrays of antennas, defined byall pair-wise combinations of transmit and receive antennas.

When a flat Rayleigh fading channel is assumed, h_(mn) arecomplex-valued Gaussian numbers with unity average power,E[h_(mn)h*_(mn)]=1. The received (baseband) vector r (see FIG. 1) isideally written as followsr=Hz=HVxwhere x=[x₁ x₂]^(T) is the vector of transmitted data streams, and noiseis not considered. Note that in a noise free channel, both streams canbe recovered perfectly if channel matrix HV is full rank. That is, twoequations and two unknowns can be solved to recover the unknowns x=[x₁x₂]^(T). When x=(HV)⁻¹r, both data streams can be recovered and link, orchannel, efficiency can be doubled.

Referring now to FIG. 3, a block diagram is provided of a wirelesscommunication system 300 in accordance with the present invention.Communication system 300 includes a base station (BS) 302 comprising amodulator and coding module 304, a codebook 306, and an antenna arraycomprising multiple antenna elements 308, 310 (two shown). Communicationsystem 300 further includes a mobile station (MS) 330, such as but notlimited to a cellular telephone, a radio telephone, a personal digitalassistant (PDA) with radio frequency (RF) capabilities, or a wirelessmodem that provides RF access to digital terminal equipment (DTE) suchas a laptop computer. MS 330 includes a channel estimator 332, acodebook 334, and an antenna array comprising multiple antenna elements336, 338 (two shown). BS 302 and MS 330 communicate via an air interface320 that includes a downlink comprising multiple downlink traffic anddownlink control channels and an uplink comprising multiple uplinktraffic and uplink control channels.

BS 302 transmits a measurement signal, that is, a midamble comprisingprecoded pilot signals, to MS 330 via multiple antennas 308, 310 and adownlink channel 322 of air interface 320. Based on the received versionof the signal, channel estimator 332 of MS 330 estimates the compositedownlink channel 322, that is, determines a frequency response Hcorresponding to the channel, and uses H to select a matrix fromcodebook 334, that is, to select one of matrices W₁, W₂, . . . , W_(N)included in the codebook.

MS 330 then conveys an indicator of the selected matrix, for example, anindex to the matrices (W₁, W₂, . . . , W_(N)) of codebook 334, and arank indicator, back to BS 302 via an uplink channel 324 of airinterface 320. Matrices (W₁, W₂, . . . , W_(N)) of codebook 334 havecorresponding matrices (W₁, W₂, . . . , W_(N)) in codebook 306. Based onthe received matrix and rank indicators, BS 302 then selects theindicated matrix, and rank of the matrix, for assigning weights to eachof the multiple antenna elements 308, 310 of the BS for a subsequenttransmission to the MS. For purposes of the present invention, basestation 302 also may be referred to herein as “the transmitter” and MS330 also may be referred to herein as “the receiver” unless specificallymentioned otherwise.

Referring now to FIG. 4, there is depicted a block diagram of basestation 302 in accordance with an embodiment of the present invention.Base station 302 comprises a multiple-stream, multiple-antennaclosed-loop transceiver that receives user data 402 and transmits theprocessed user data using an antenna array 432 that comprises themultiple antenna elements 308, 310.

User data 402 enters a data splitter 404, which separates the user datastream into a plurality of data streams, such as data stream 406 anddata stream 408. While two data streams are shown in FIG. 4, datasplitter 404 may produce any number of data streams. Data splitter 404splits data 402 in proportion to a control signal 442, which is producedby a controller 440. For example, control signal 442 may specify a ratioof 2-to-1, wherein two bits are sent to data stream 406 and one bit issent to data stream 408. This splitting ratio may specify an equalnumber of bits on both streams, or all data bits may be sent to onestream.

Data streams 406 and 408 output by data splitter 404 are input intomultiple forward error correction encoders (FEC) 410 and 412. Theseerror correction encoders may be implemented with a convolutionalencoder, a turbo encoder, a block encoder, or the like. The type ofencoding and the rate of encoding are controlled by a control signal444, which is output by controller 440. Control signal 444 may set errorcorrection encoders 410 and 412 to the same error encoding schemes ordifferent encoding schemes.

Outputs of error correction encoders 410 and 412 are coupled to inputsof modulators 414 and 416. Modulators 414 and 416 may be implementedwith linear or non-linear modulation schemes, including all varieties ofmodulators that modulate amplitude and phase, and combinations ofamplitude and phase. Examples of modulators that may be used includeBinary Phase Shift Keying modulators (BPSK), Quadrature Phase ShiftKeying modulators (QPSK), M-ary phase shift keying modulators, M-aryquadrature amplitude modulators (MQAM), and the like.

Controller 440 further produces a control signal 446 that is used toselect a type of modulation used in modulators 414 and 416. Themodulation schemes in the data streams may be the same, or different.The output of modulators 414 and 416 are coupled to inputs of optionalspreaders 420 and 422, respectively. Spreaders 420 and 422 each spreadsthe signal using a spreading code 418, such as a Walsh code, that isassigned to user data 402.

Outputs of optional spreaders 420 and 422 are coupled to inputs of apower allocator 424. Power allocator 424 sets a power ratio between datastreams 406 and 408 in response to a control signal 448 from controller440. Power allocator 424 may allocate all power to one data stream,equal powers on data streams, or other ratios of unequal powerallocations.

Outputs of power allocator 424 are coupled to inputs of antenna arraysignal processor 426, which further processes the data streams byapplying antenna array weight sets to each data stream. These antennaarray weight sets come from controller 440 via a control signal 450. Byapplying the antenna array weight sets to data streams 406 and 408,antenna array signal processor 426 enables the transmission of each datastream with a different antenna array beamforming pattern.

The outputs of antenna array signal processor 426 include weightedcomponents of the input data streams. For example, output 428 mayinclude a phase-and-gain weighted portion of data stream 406 addedtogether with a phase-and-gain weighted portion of data stream 408. Thenumber of weighted outputs 428, 430 from antenna array signal processor426 is equal to the number of transmit antennas 308, 310. While thenumber of outputs of antenna array signal processor 426 may be greaterthan the number of data streams input, the number of data streamstransmitted remains the same.

Referring now to FIG. 5, there is depicted a block diagram of antennaarray signal processor 426 in accordance with an embodiment of thepresent invention. As shown, data streams 406 and 408 enter antennaarray signal processor 426, wherein a copy of each data stream is sentto a gain multiplier corresponding to an antenna element that will beused in an antenna array. In the example shown in FIG. 5, two antennaswill be used in the antenna array, therefore copies of each data streamare sent to two gain multipliers 502. Following each gain multiplier 502is a phase shifter 508, which rotates the phase of the signal accordingto the control signal 450 received from controller 440. Outputs of phaseshifters 508 are coupled to summers 510, which add the weighted datastreams to produce output signals 428 and 430. Output signals 428 and430 then may be up-converted, amplified, and coupled to thecorresponding antenna elements 308, 310.

Control signal 450 includes multiple antenna array weight sets, whereinone antenna array weight set is associated with each data stream. Forexample, control signal 450 includes weight set signals 504 and 506.Weight set signal 504 includes gain and phase weights (that is, complexweights) for each gain multiplier 502 and phase shifter 508 associatedwith data stream 406. Thus, the outputs of phase shifters 508 associatedwith data stream 406 produce antenna signals that provide a selectedantenna pattern for data stream 406. Similarly, weight set signal 506includes phase and gain weights for each gain multiplier 502 and phaseshifter 508 associated with data stream 408. In the outputs of phaseshifters 508 associated with data stream 408 produce antenna signals fordriving an antenna array with a selected pattern for data stream 408.

In order to produce desired antenna beamformed patterns for each datastream, gain multipliers 502 associated with a data stream may havedifferent gain values and phase shifters 508 associated with a datastream may have different phase shift values, whereby producing antennasignals that work together to form a particular transmission pattern.

Controller 440 outputs control signals 442, 444, 446, 448, and 450 basedupon information received from a feedback receiver 434 and data storedin a memory 460. Feedback receiver 434 is shown coupled to a separateantenna for receiving feedback data from a remote receiver, such as MS330; however, one of ordinary skill in the art realizes that one of theantenna elements of antenna array 432 may be used to receive thefeedback data. Feedback data from feedback receiver 434 includes acodebook index and may further include a rank index, as described below,which are used by controller 440 to lookup transmission weightings incodebook 306 pre-stored within memory 460. Controller 440 also may beused to calculate, or derive, additional control signals or transmissionparameters based upon feedback data. Therefore, it should be understoodthat feedback data may include measurements upon which calculations maybe based, or data that indicates parameters to be used by base station302.

Referring now to FIG. 6, there is depicted a block diagram of MS 330 foruse in the multiple-stream, multiple-antenna transceiver system 300 inaccordance with an embodiment of the present invention. MS 330 comprisesa multiple-stream, multiple-antenna transceiver that includes an antennaarray 602 having multiple antenna elements 336, 338 that receive radiofrequency (RF) signals transmitted by base station 302. The received RFsignals are most likely different signals because antenna elements 336,338 are spaced apart, and propagation paths taken by received RF signalsfrom antenna elements 308, 310 of base station 302 are most likelydifferent in a multi-path fading environment.

In the multiple-stream, multiple-antenna transceiver system that is madeup of base station 302 and MS 330, multiple data streams are transmittedto increase the data throughput between the base station and MS. Basestation 302 is able to simultaneously transmit multiple data streams,and MS 330 is able to keep the multiple streams separate by exploitingthe differences in the channel characteristics between the multipleantennas at the base station and MS. Thus, user data 402 in base station302 is received by MS 330 and output as estimated user data 640.

The received RF signals are input into an RF receiver front end 604,wherein the RF signals are down converted and digitized. The output ofRF receiver front end 604 is a stream of complex baseband digitalsamples that represent the received RF signals.

The outputs of RF receiver front end 604 are input into a receiversignal processor 606, which has the function of separating data streams406 and 408 in MS 330. In one embodiment of the present invention,receiver signal processor 606 may be implemented by multiplying theinput signals by the complex conjugate transpose of a unitary matrix T,which is the left singular vectors of the singular value decompositionof the composite channel matrix H. In another embodiment of the presentinvention, receiver signal processor 606 may be implemented bymultiplying the input signals by the pseudo-inverse of the product ofthe composite channel matrix H with the matrix V. In yet anotherembodiment of the present invention, receiver signal processor 606 maybe implemented by multiplying the input signals by MMSE combiningweights calculated from the product of the composite channel matrix Hwith the matrix V. Receiver signal processor 606 is controlled by acontrol signal 622 from a controller 620.

The data streams output by receiver signal processor 606 are input tooptional despreaders 610 and 612, which despread the signals using thesame spreading code 608 used in base station 302. The outputs ofdespreaders 610 and 612 are coupled, respectively, to the inputs ofdemodulator and decoders 614 and 616. Each demodulator and decoder 614and 616 demodulates the signal and decodes the signal using demodulationand error correction decoding techniques that correspond to thoseselected for each data stream in the transmitter.

The outputs from demodulator and decoders 614 and 616 are input into acombiner 618, which combines the multiple streams received back into asingle stream for output as estimated user data 640. Combiner 618operates under the control of controller 620, as directed by controlsignal 626. Because the received data streams may have different datarates, and because one data stream may have a data rate equal to zero,combiner 618 must reconstruct the user data in accordance with the waydata was originally split by data splitter 404 in base station 302.

In order to control the transmission of multiple data streams viamultiple antennas at base station 302, MS 330 must measure the compositechannel and send feedback data to the base station. As shown, outputs ofradio frequency front end 604 are also coupled to composite channelestimator 332, which uses the pilot signals transmitted from eachantenna element 310, 312 in base station 302 to measure the compositechannel between the multiple transmit antenna elements and the multiplereceive antenna elements. In practice, MS 330 receives the downlinkpilot signals and measures the downlink channel estimates from each ofthe base station's (transmit) antenna elements to each of the (receive)antenna elements 336, 338 of the MS.

The output of composite channel estimator 332, which is represented bythe H matrix, is input into signal-to-noise ratio (SNR) computer andpower allocator 630 and feedback transmitter 634. SNR computer and powerallocator 630 computes an SNR for each data stream hypotheticallytransmitted. Based upon the SNR computations, the power allocationfunction of block 630 allocates power to each data stream. Once powerhas been allocated to each data stream, final SNR calculations may beperformed using the selected power allocation.

A modulator and coder 632 receives information from SNR computer andpower allocator 630 and uses the information to select an encodingscheme and a modulation scheme to be used in base station 302.Generally, higher order modulators are selected for data streams havinghigh signal-to-noise ratios.

Feedback transmitter 634 receives information from composite channelestimator 332, SNR computer and power allocator 632, and modulator andcoder selector 630. This information represents calculations andselections made in MS 330 that will be used to control the transmissionmodes of base station 302. In a preferred embodiment, feedbacktransmitter 634 analyzes the data and selects a codebook value (indexand rank) and associated transmitter parameters that most closely matchthe transmitter parameters represented by the input data. Therefore,feedback transmitter 634 includes, or is coupled to, a memory thatstores a codebook 334 for producing a codebook index that is transmittedto base station 302 via one or more transmit antennas. Although thetransmit antenna is shown separate from receive antenna array 602, thetransmit antenna may be one of the antenna elements 308, 310 in antennaarray 602. Data transmitted by feedback transmitter 634 is received inbase station 302 by feedback receiver 434.

In an embodiment of the present invention, codebook-based feedback ofchannel information enables linear pre-coding (including beamforming) inMIMO systems, in a TDD or a FDD scenario. Base station 302 as well as MS330 have prior knowledge of a fixed, predetermined set of pre-codingmatrices, that is, a codebook. Base station 302 transmits a known signalprecoded with a precoding matrix, that is, a midamble comprisingprecoded pilot signals, to MS 330. Based on the received precoded pilotsignals, MS 330 estimates the downlink channel 322 and, based on theestimate, selects a particular codebook entry, that is, a codebookmatrix and rank. An index of this entry is sent back to base station 302using a low-rate feedback channel 324. In order to reduce thecomputational complexity necessary at MS 330 for choosing the codeword,the present invention provides for a pre-coding of the pilot signal thatis received by, and measured by, MS 330 and used by the MS to select thecodebook entry that is fed back to base station 302. Further, thepre-coding of the pilot signal is such that MS 330 does not need to beinformed, in advance of receiving the midamble, of the particular matrixthat is used to pre-code of the midamble in order for the pre-coding tobe useful to the MS.

Referring now to FIG. 7, a logic flow diagram 700 is provided forpre-coding of a pilot signal by communication system 300 in accordancewith an embodiment of the present invention. Logic flow diagram 700begins (702) when base station 302 generates (704) a predeterminedcodeword, preferably a pilot pattern, that is, a predetermined patternof bits that is known to both the base station and MS 330 and that isused for channel estimation. As is known in the art, a pilot pattern isused as a training sequence for channel estimation, power measurements,and/or synchronization. Base station 302 applies the pilot pattern tosplitter 404 to produce (706) multiple parallel pilot patterns andproceeds to process the pilot patterns in accordance with knowntechniques, as described above with respect to FIG. 4, to producemultiple parallel pilot patterns that are applied to the inputs ofantenna array signal processor 426. Antenna array signal processor 426then pre-codes (710) the multiple pilot patterns by applying antennaarray weight sets to each pilot pattern of the multiple pilot patternsto produce a pre-coded pilot signal comprising multiple parallel,pre-coded multiple pilot patterns.

These antenna array weight sets come from controller 440 via a controlsignal 450; however, unlike transmitted user data where the weight setsare selected based on feedback from the MS, controller 440 may select(708) a unitary matrix for weighting, or pre-coding, of the pilot signalwithout the use of feedback from the MS. Any unitary matrix may be used;the unitary matrix may or may not be contained in the codebooks 306, 334and base station 302 may arbitrarily determine the unitary matrix usedto weight the predetermined codeword. Further, MS 330 may or may notknow in advance, or be informed by the base station, of the particularunitary matrix selected by the base station. Base station 302 thentransmits (712) the pre-coded pilot signal to MS 330 via the multipleantenna elements 308, 310 of antenna array 432 and downlink channel 322.

MS 330 receives (714) the pre-coded pilot signal via the multipleantenna elements 336, 338 of antenna array 602 and estimates (716)channel 322 based on the received pre-coded pilot signal. Based on theestimated channel, MS 330 then determines an effective channel for eachof one or more matrices of codebook 334. MS 330 then selects (718) apreferred codebook matrix and rank for use by base station 302 in asubsequent transmission of user data based on the effective channeldeterminations, and in particular by choosing a preferred codebookmatrix corresponding to the best effective channel. MS 330 then informs(720) base station 302 of the selected codebook matrix and rank,preferably by conveying a codebook index to the preferred codebookmatrix, and a rank index, back to the base station. Base station 302then uses (722) the selected codebook matrix and rank to weight asubsequent transmission of user data to MS 330, and logic flow diagram700 then ends (724).

A brief description of codebook formation can now be described here.Assume that base station 302 has M_(t) antennas, MS 330 has M_(r)antennas, and that M_(s) data-streams are to be transmitted by the basestation to the MS. Let H(k) represent the M_(r)×M_(t) channel matrix forthe k-th subcarrier in frequency. Let W represent a pre-coding matrix ofdimension M_(t)×M_(s) which is an element of the codebook as definedherein (note that this W is different from the W 404, 608 used inspreaders 420 and 422 and despreaders 610 and 612). The criteria forselecting a codeword by a receiver is non-unique but usually theselection criteria involve multiplications of the form H(k)W.

A formula for selecting an element of a codebook by a receiver may beexpressed as

$V = {\underset{W \in \Phi}{\arg\;\max}{\sum\limits_{k = 1}^{K}{{{H(k)}W}}_{F}^{2}}}$where the matrix norm is the Frobenius norm (∥A∥_(F) ² means the sum ofthe squared magnitude of the entries of A), H(k) represents theM_(r)×M_(t) channel matrix for a k-th subcarrier in frequency, K denotesthe size of the cluster consisting of K adjacent subcarriers, W is aprecoding matrix of dimension M_(t)×M_(s), Φ={W₁, W₂, . . . , W_(N)}denotes the codebook of precoding matrices, and V is the selectedelement from Φ that represents the quantized precoding matrix for thecluster. The present invention provides for the construction of Φ from aset of unitary matrices.

A standard and fast way of evaluating codebooks is to compute theminimum pairwise distances of all the codewords. The distance measuresused are summarized below.

$d_{\min,k} = {\min\limits_{W_{i},W_{j},{i \neq j}}{\frac{1}{\sqrt{2}}{{{W_{i}W_{i}^{H}} - {W_{j}W_{j}^{H}}}}_{F}}}$where the subscript k denotes the number of streams (or rank). Thisdistance is used for 1≦k<M_(t). The following distance is used fork=M_(t).

$d_{\min,k} = {\min\limits_{W_{i},W_{j},{i \neq j}}{{{W_{i} - W_{j}}}_{F}.}}$A codebook having a larger d_(min,) _(k) is considered to be better thana competitor codebook. The equivalence relations for certain selectioncriteria are as follows:

${\underset{W}{\arg\;\max}{{HW}}_{F}^{2}} = {\underset{W}{\arg\;\max}{{HW}_{\bot}}_{F}^{2}}$${\log_{2}{\det\left\lbrack {I + {\frac{E_{s}}{M_{s}N_{0}}W^{H}H^{H}{HW}}} \right\rbrack}} = {\log_{2}{\det\left\lbrack {I + {\frac{E_{s}}{M_{s}N_{0}}H^{H}H} - {\frac{E_{s}}{M_{s}N_{0}}H^{H}{HW}_{\bot}W_{\bot}^{H}}} \right\rbrack}}$${{trace}\left\lbrack {I + {\frac{E_{s}}{M_{s}N_{0}}W^{H}H^{H}{HW}}} \right\rbrack}^{- 1} = {r - M_{r} + {{trace}\left\lbrack {I + {\frac{E_{s}}{M_{s}N_{0}}{HH}^{H}} - {\frac{E_{s}}{M_{s}N_{0}}{HW}_{\bot}W_{\bot}^{H}H^{H}}} \right\rbrack}^{- 1}}$where w_(|) is of rank (M_(t)−r) and denotes the orthogonal complementof w, where r denotes the rank or the number of streams (interchangeablydenoted by M_(s)). Thus, in case a simple codebook exists for w_(⊥) andnot for w, it is beneficial to search over codebooks consisting ofw_(⊥). Note that other distances can be used. One such alternative is touse the square root of one minus minimum squared singular value of W₁^(H)W₂.

An index of the selected pre-coded set of weights is then sent back tothe base station, whereupon the base station checks that index againstthe codebook stored in memory to select the indicated set of weights insubsequent transmissions. For a rank ‘n’ transmission, the base stationuses the first n columns of selected matrices as the beamformingweights.

In order to facilitate the selection of a codebook matrix based on aunitary matrix that is used to pre-code the midamble, unitary matricesare used to construct codebooks 306 and 334, starting with a unitarymatrix U that is used as a building block for the codebook. Unitarymatrix U may be any unitary matrix; however, whatever matrix serves as Uis used to precode the midamble.

For example, the following describes a scheme for codebook constructionfor four transmit (Tx) antenna elements using a unitary matrix U. Thisscheme then may be extended to a scheme for codebook construction foreight transmit antenna elements, and so on. For the four antenna elementscheme, four unitary matrices, that is, A, B, C, D (corresponding to acodebook size of 16) are defined as:A=U,B=UA₁,C=UA₂,D=UA₃   (1)where U can be an arbitrary 4×4 unitary matrix and matrices A₁, A₂, A₃are defined in equations (2), (3) and (4).

$\begin{matrix}{A_{1} = {\left( \frac{1}{\sqrt{2}} \right)\begin{bmatrix}0 & 1 & 0 & i \\i & 0 & 1 & 0 \\0 & i & 0 & 1 \\1 & 0 & i & 0\end{bmatrix}}} & (2) \\{A_{2} = {\left( \frac{1}{\sqrt{2}} \right)\begin{bmatrix}0 & 1 & 0 & i \\0 & i & 0 & 1 \\i & 0 & 1 & 0 \\1 & 0 & i & 0\end{bmatrix}}} & (3) \\{A_{3} = {\left( \frac{1}{\sqrt{2}} \right)\begin{bmatrix}0 & 1 & 0 & i \\i & 0 & 1 & 0 \\1 & 0 & i & 0 \\0 & i & 0 & 1\end{bmatrix}}} & (4)\end{matrix}$Note that matrices A₁, A₂ and A₃ have only two non-zero entries (1 or i)in each column. So the columns of matrices B, C and D are linearcombinations of two columns of U. From matrices A, B, C, D, a codebook Φof cardinality 16 may be constructed, that is, Φ={A₀, A₁, A₂, A₃, B₀,B₁, B₂, B₃, C₀, C₁, C₂, C₃, D₀, D₁, D₂, D₃}, where A_(j) representsmatrix A with the columns shifted circularly to the left by j places.The codebook Φ is designed as a common codebook for rank-1, rank-2,rank-3 and rank-4 precoding matrices. In the case of rank-1, the firstcolumn of each of the matrices constitute a codebook, in the case ofrank-2 the first two columns of each matrix constitute the codebook andso on. The distance properties of such a codebook are given in Table 1:

TABLE 1 Distance metric comparison for 4Tx size 16 codebook Rank-1Rank-2 Rank-3 Rank-4 MUB 0.8660 1.0 0.8660 1.4142 LTE 0.7071 1.0 0.70711.4142 Proposed 0.7071 1.0 0.7071 1.0824 Inventionwhere MUB refers to codebook design pursuant to an article by B. Mondal,T. A. Thomas, M. Harrison, “Rank Independent Codebook Design from aQuaternary Alphabet”, presented at the IEEE Asilomar Conference onSignals, Systems, and Computers, pg. 297-301, Pacific Grove, Calif.,USA, Nov. 4-7, 2007, and LTE refers to codebook design pursuant to theThird Generation Partnership Long Term Evolution (3GPP LTE) standards.In simulations depicted in FIG. 8, the 4×4 unitary matrix U was chosento be:

$\begin{matrix}{U = {\left( \frac{1 + i}{2\sqrt{2}} \right)\begin{bmatrix}1 & 1 & 1 & 1 \\1 & 1 & {- 1} & {- 1} \\1 & {- 1} & {- 1} & 1 \\1 & {- 1} & 1 & {- 1}\end{bmatrix}}} & (5)\end{matrix}$

In the case of eight transmit (Tx) antennas (that is, M_(t)=8), eightunitary matrices A, B, C, D, E, F, G, H can be defined as:A=U,B=UA₁,C=UA₂,D=UA₃,E=UA₄,F=UA₅,G=UA₆,H=UA₇   (6)where U is an arbitrary 8×8 unitary matrix and matrices A₁, . . . , A₇are defined in equations (7)-(13) below.

The matrices A₁, . . . , A₇ defined in equations (7)-(13) and thematrices A1, A₂, A₃ as defined in equations (2), (3) and (4) arenon-unique and there exist multiple choices for such matrices with theproperty that the entries are limited to a restricted alphabet.Restricted alphabet refers to an alphabet that consists of 0 and integerpowers of i (sqrt(−1)) or half integer powers of i. Restricted alphabetalso refers to an alphabet that consists of integer powers of i(sqrt(−1)) or half integer powers of i. In one embodiment, the alphabetscomprise the values {0, 1, −1, i, −i, (1+i)/sqrt(2), (1−i)/sqrt(2),(−1+i)/sqrt(2), (−1−i)/sqrt(2)} where sqrt(2) means the square root of2. One may note that, in this example, the set contains 0 and thefollowing integer and half integer powers of i: {0, 2, 1, 3, ½, 7/2,3/2, and 5/2}. In another embodiment, the alphabets comprise the values{0, 1, −1, i, −i}. In yet another embodiment, the alphabets comprise thevalues {1, −1, i, −i}. In still another embodiment, the alphabetscomprise the values {1, −1, i, −i, (1+i)/sqrt(2), (1−i)/sqrt(2),(−1+i)/sqrt(2), (−1−i)/sqrt(2)}. It may also be noted that the matricesA₁, A₂, A₃ may be scaled by a constant factor.

$\begin{matrix}{A_{1} = {\left( \frac{1}{\sqrt{2}} \right)\begin{bmatrix}0 & 0 & 0 & i & 0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 & 0 & 0 & i & 0 \\0 & i & 0 & 0 & 0 & 1 & 0 & 0 \\1 & 0 & 0 & 0 & i & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 & 0 & i \\0 & 0 & i & 0 & 0 & 0 & 1 & 0 \\0 & 1 & 0 & 0 & 0 & i & 0 & 0 \\i & 0 & 0 & 0 & 1 & 0 & 0 & 0\end{bmatrix}}} & (7) \\{A_{2} = {\left( \frac{1}{\sqrt{2}} \right)\begin{bmatrix}0 & 0 & 0 & i & 0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 & 0 & 0 & i & 0 \\0 & i & 0 & 0 & 0 & 1 & 0 & 0 \\1 & 0 & 0 & 0 & i & 0 & 0 & 0 \\i & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & i & 0 & 0 \\0 & 0 & i & 0 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 1 & 0 & 0 & 0 & i\end{bmatrix}}} & (8) \\{A_{3} = {\left( \frac{1}{\sqrt{2}} \right)\begin{bmatrix}0 & 0 & 0 & i & 0 & 0 & 0 & 1 \\0 & 0 & 0 & 1 & 0 & 0 & 0 & i \\0 & 0 & 1 & 0 & 0 & 0 & i & 0 \\0 & 0 & i & 0 & 0 & 0 & 1 & 0 \\0 & i & 0 & 0 & 0 & 1 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & i & 0 & 0 \\1 & 0 & 0 & 0 & i & 0 & 0 & 0 \\i & 0 & 0 & 0 & 1 & 0 & 0 & 0\end{bmatrix}}} & (9) \\{A_{4} = {\left( \frac{1}{\sqrt{2}} \right)\begin{bmatrix}0 & 0 & 0 & i & 0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 & 0 & 0 & i & 0 \\0 & 0 & 0 & 1 & 0 & 0 & 0 & i \\0 & 0 & i & 0 & 0 & 0 & 1 & 0 \\0 & i & 0 & 0 & 0 & 1 & 0 & 0 \\1 & 0 & 0 & 0 & i & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & i & 0 & 0 \\i & 0 & 0 & 0 & 1 & 0 & 0 & 0\end{bmatrix}}} & (10) \\{A_{5} = {\left( \frac{1}{\sqrt{2}} \right)\begin{bmatrix}0 & 0 & 0 & i & 0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 & 0 & 0 & i & 0 \\0 & 0 & i & 0 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 1 & 0 & 0 & 0 & i \\0 & i & 0 & 0 & 0 & 1 & 0 & 0 \\1 & 0 & 0 & 0 & i & 0 & 0 & 0 \\i & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & i & 0 & 0\end{bmatrix}}} & (11) \\{A_{6} = {\left( \frac{1}{\sqrt{2}} \right)\begin{bmatrix}0 & 0 & 1 & 0 & 0 & 0 & i & 0 \\0 & 0 & 0 & i & 0 & 0 & 0 & 1 \\1 & 0 & 0 & 0 & i & 0 & 0 & 0 \\0 & i & 0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 & 0 & i \\0 & 0 & i & 0 & 0 & 0 & 1 & 0 \\0 & 1 & 0 & 0 & 0 & i & 0 & 0 \\i & 0 & 0 & 0 & 1 & 0 & 0 & 0\end{bmatrix}}} & (12) \\{A_{7} = {\left( \frac{1}{\sqrt{2}} \right)\begin{bmatrix}0 & i & 0 & 0 & 0 & 1 & 0 & 0 \\1 & 0 & 0 & 0 & i & 0 & 0 & 0 \\0 & 0 & 0 & i & 0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 & 0 & 0 & i & 0 \\0 & 0 & 0 & 1 & 0 & 0 & 0 & i \\0 & 0 & i & 0 & 0 & 0 & 1 & 0 \\0 & 1 & 0 & 0 & 0 & i & 0 & 0 \\i & 0 & 0 & 0 & 1 & 0 & 0 & 0\end{bmatrix}}} & (13)\end{matrix}$

Thus a 64 element eight dimensional codebook Ψ may then be constructedsimilarly to the four dimensional codebook described above by circularlyshifting the columns of these eight matrices, that is, Ψ={A₀, . . . ,A₇, B₀, . . . , B₇, C₀, . . . , C₇, D₀, . . . , D_(7,) E₀, . . . , E₇,F₀, . . . , F₇, G₀, . . . , G₇, H₀, . . . , H₇}. In the case of rank-1,the first column of each of the matrices constitute a codebook, in thecase of rank-2 the first two columns of each matrix constitute thecodebook and so on. The distance properties of such a codebook are givenin Table 2:

TABLE 2 Distance metric comparison for 8Tx size 64 codebook Rank-1Rank-2 Rank-3 Rank-4 MUB 0.9354 1.0 1.0 1.0 Proposed 0.7071 1.0 1.0 1.0Invention

FIG. 8 shows error rate results from simulations comparing theperformances of various codebooks. The results show that the unitarymatrix-based codebooks described herein have very similar error rateperformance as the LTE codebooks.

In the simulations, the 8×8 unitary matrix U was chosen to be:

$\begin{matrix}{U = {\left( \frac{1 + i}{4} \right)\begin{bmatrix}1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\1 & {- 1} & 1 & 1 & {- 1} & 1 & {- 1} & {- 1} \\1 & 1 & 1 & {- 1} & 1 & {- 1} & {- 1} & {- 1} \\1 & 1 & {- 1} & 1 & {- 1} & {- 1} & {- 1} & 1 \\1 & {- 1} & 1 & {- 1} & {- 1} & {- 1} & 1 & 1 \\1 & 1 & {- 1} & {- 1} & {- 1} & 1 & 1 & {- 1} \\1 & {- 1} & {- 1} & {- 1} & 1 & 1 & {- 1} & 1 \\1 & {- 1} & {- 1} & 1 & 1 & {- 1} & 1 & {- 1}\end{bmatrix}}} & (14)\end{matrix}$

The use of the above described codebook design and precoding of a pilotpattern using the unitary matrix U can enable two types of feedbackstrategies—(i) conventional codebook-based feedback strategy based onmidamble or broadcast pilots, and (ii) mix of beam selection andcodebook feedback.

Referring now to FIGS. 7 and 9, a logic flow diagram 900 is providedthat illustrates a method performed by MS 330 in determining aneffective channel for the matrices of codebook 334 in accordance with anembodiment of the present invention. Let codebooks Φ and Ψ have 8-PSKentries. Logic flow diagram 900 then begins (902) when MS 330 determines(904) an effective channel for a subset ‘S’ of rank-1 codebook indicesto produce ‘S’ effective channels. That is, assume w to be a rank-1codeword chosen from a codebook and H to be a M_(r)×M_(t) channelmatrix, where M_(t) is the number of transmit antenna elements (that is,at base station 302) and M_(r) is the number of receive antenna elements(that is, at MS 330). Then the computation for Hw can be considered as abasic unit of computation.

MS 330 then determines (906) an effective channel for the remainingcodebook indices as a function of the ‘S’ effective channels. That is,codebook Φ has 16 unique vectors and Ψ has 64 unique vectors for allranks. Once the rank-1 Hw computations are performed for all the indicesthere is no need for any additional Hw computations for the remainingranks. The codebook search for Φ and Ψ then can be simplified byordering the computations. For codebook Φ, assume that the Hwcomputations are completed for the first 4 indices (all the columns ofU). Each of the Hw computations for the remaining 12 indices can beobtained by a complex addition using the Hw results obtained for thefirst 4 indices. In the case of codebook Ψ, after the computations forthe first 8 indices are completed, each of the Hw computations for theremaining 56 indices can be obtained by a complex addition using the Hwresults obtained for the first 8 indices. Logic flow diagram 900 thenends (908). This mode of feedback may provide modest gains incomputation compared to the LTE codebook in the case of four Txantennas; however, in the case of eight Tx antennas the computationalsavings will be significant.

For a strategy with a mix of beam selection and codebook feedback, thepilots for the midamble may be precoded by a unitary matrix U that isdetermined by base station 302. Then, the Hw computations for the first4 indices of Φ and the first 8 indices of Ψ can be eliminated becausethey are multiplied by the downlink channel naturally. This would alsomean that U need not be standardized or known by MS 330. As a result, Ucan be controlled by base station 302 and set according to antennapolarizations or long-term antenna correlations, or randomized betweencell sites and the codebook is no longer restricted to an 8-PSKalphabet. This mode of operation will also provide maximum savings interms of computation.

In one embodiment of the invention a base station, such as base station302, may employ a precoding matrix U to modify the codebook that isalready built into mobile stations, such as MS 330, as necessitated bythe standard specifications. This precoding matrix U may be optimized toimprove the cell throughput by matching the modified codebook to aparticular antenna configuration at the base station or multi-pathfading environment or traffic type or to reduce interference. The choiceof U may change with time or frequency or both.

In another embodiment of the invention, multiple base stations ormultiple sectors may coordinate the choice of the precoding matrix Uthat is used by each base station, such as base station 302, or sectorto precode the mid-amble. The choice of U may be optimized to minimizeinter-cell or inter-sector interference.

In yet another embodiment of the invention, an MS, such as MS 330, mayestimate the interference from the precoded mid-amble (or precodedpilots) received from a non-serving base station. This estimate may beused by the MS to feed back a codebook index to a serving base station,such as base station 302.

In still another embodiment of the invention, an MS, such as MS 330, mayestimate the interference from the precoded midamble (or precodedpilots) received from a serving base station, such as base station 302.The MS then may use this interference estimate to determined, and feedback, a codebook index to the serving base station.

Thus the present invention provides for a less computationally intensivescheme of codebook-based feedback of channel information, enablinglinear pre-coding (including beamforming) in MIMO systems, in a TDD or aFDD scenario. Base station 302 transmits a known signal, precoded with aprecoding matrix, that is, a midamble comprising precoded pilot signals,to MS 330. Based on the received precoded pilot signals, MS 330estimates the downlink channel 322 and, based on the estimate, selects aparticular codebook entry, that is, a codebook matrix and rank. An indexof this entry is sent back to base station 302 using a low-rate feedbackchannel 324. In order to reduce the computational complexity necessaryat MS 330 for choosing the codeword, the present invention provides fora pre-coding of the pilot signal that is received by, and measured by,MS 330 and used by the MS to select the codebook entry that is fed backto base station 302. Further, the pre-coding of the pilot signal is suchthat MS 330 does not need to be informed, in advance of receiving themidamble, of the particular matrix that is used to pre-code of themidamble in order for the pre-coding to be useful to the MS.

The invention can be implemented in any suitable form includinghardware, software, firmware or any combination of these. The inventionmay optionally be implemented partly as computer software running on oneor more data processors and/or digital signal processors. The elementsand components of an embodiment of the invention may be physically,functionally and logically implemented in any suitable way. Indeed thefunctionality may be implemented in a single unit, in a plurality ofunits or as part of other functional units. As such, the invention maybe implemented in a single unit or may be physically and functionallydistributed between different units and processors.

While the present invention has been particularly shown and describedwith reference to particular embodiments thereof, it will be understoodby those skilled in the art that various changes may be made andequivalents substituted for elements thereof without departing from thescope of the invention as set forth in the claims below. Accordingly,the specification and figures are to be regarded in an illustrativerather then a restrictive sense, and all such changes and substitutionsare intended to be included within the scope of the present invention.

Benefits, other advantages, and solutions to problems have beendescribed above with regard to specific embodiments. However, thebenefits, advantages, solutions to problems, and any element(s) that maycause any benefit, advantage, or solution to occur or become morepronounced are not to be construed as a critical, required, or essentialfeature or element of any or all the claims. As used herein, the terms“comprises,” “comprising,” or any variation thereof, are intended tocover a non-exclusive inclusion, such that a process, method, article,or apparatus that comprises a list of elements does not include onlythose elements but may include other elements not expressly listed orinherent to such process, method, article, or apparatus. Furthermore,unless otherwise indicated herein, the use of relational terms, if any,such as first and second, top and bottom, and the like are used solelyto distinguish one entity or action from another entity or actionwithout necessarily requiring or implying any actual such relationshipor order between such entities or actions.

1. A method for providing feedback for closed-loop transmitting with aplurality of transmit antenna elements and a plurality of receiveantenna elements, the method comprising: providing a codebook containingsets of weightings for the plurality of transmit antenna elements witheach set of weightings identified by an index and the codebook known toa transmitter and a receiver; pre-coding pilot signals using a precodingmatrix to produce pre-coded pilot signals; transmitting the pre-codedpilot signals to the receiver via the plurality of transmit antennaelements; and in response to transmitting the pre-coded pilot signals,receiving at the transmitter an index to a set of weightings in thecodebook for use in a subsequent transmission of a data stream, whereinthe pre-coding pilot signals comprises pre-coding pilot signals using aunitary matrix and further, wherein the receiver is not informed, by thetransmitter, of the unitary matrix used to pre-code the pilot pattern.2. The method of claim 1, further comprising: receiving the pre-codedpilot signals; estimating a composite channel between the plurality oftransmit antenna elements and the plurality of receive antenna elementsbased on the received pre-coded pilot signals; selecting a set ofweightings based on the composite channel estimates; and feeding back anindex of the set of weightings to a transmitter associated with theplurality of transmit antenna elements for use in a subsequenttransmission of a data stream.
 3. The method of claim 1, wherein thecodebook weights are restricted to a finite alphabet.
 4. The method ofclaim 1, wherein the same codebook is used for all ranks
 5. A method forproviding feedback for closed-loop transmitting with a plurality oftransmit antenna elements and a plurality of receive antenna elements,the method comprising: receiving pre-coded pilot signals; determiningeffective channels for a subset of rank-1 codebook weightings to produce‘S’ effective channels; and determining an effective channel for eachremaining codebook weightings as a low complexity function of the ‘S’effective channels.
 6. The method of claim 5, further comprising:selecting a set of weightings based on the determined effectivechannels; and feeding back an index of the set of weightings to atransmitter associated with the plurality of transmit antenna elementsfor use in a subsequent transmission of a data stream.
 7. A base stationcapable of operating in a multiple input, multiple output communicationsystem, the base station comprising: an antenna array comprisingplurality of antenna elements; a codebook containing sets of weightingsfor the plurality of transmit antenna elements with each set ofweightings identified by an index known to the base station and a mobilestation serviced by the base station; an antenna array signal processorthat pre-codes pilot signals using a matrix to produce pre-coded pilotsignals that is transmitted via the plurality of transmit antennaelements; and a receiver that receives an index to a set of weightingsin the codebook for use in a subsequent transmission of a data stream,wherein the antenna array signal processor pre-codes the pilot signalsusing a unitary matrix and further, wherein the mobile station is notinformed, by the base station, of the unitary matrix used to pre-codethe pilot pattern.
 8. The base station of claim 7, wherein the codebookweights are restricted to a finite alphabet.
 9. The base station ofclaim 7, wherein the same codebook is used for all ranks
 10. A systemcomprising the base station of claim 7, and further comprising a mobilestation having a plurality of antenna elements and that is configured toreceive the pre-coded pilot signal, estimate a composite channel betweenthe plurality of transmit antenna elements and the plurality of receiveantenna elements based on the received pre-coded pilot signal, selectinga set of weightings for each data stream based on the composite channelestimate, and feed back an index of the set of weightings to atransmitter associated with the plurality of transmit antenna elementsfor use in subsequent transmissions of a data stream.
 11. A mobilestation capable of operating in a multiple input, multiple outputcommunication system, the mobile station comprising a plurality ofantenna elements and configured to receive a pre-coded pilot signal,based on the received pilot signal, determine an effective channel for asubset of rank-1 codebook weightings to produce ‘S’ effective channels,and determine an effective channel for each remaining codebookweightings as a function of the ‘S’ effective channels.
 12. The mobilestation of claim 11, wherein the mobile station is further configured toselect a set of weightings based on the determined effective channelsand feed back an index of the set of weightings to a transmitter for usein a subsequent transmission of a data stream.